{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import * "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "平方误差可以写作：\n",
    "$$\\sum_{i=1}^{n}(y_{i}-x^{T}_{i}w)^{2}$$\n",
    "用矩阵表示可以写作：\n",
    "$$(y-Xw)^{T}(y-Xw)$$\n",
    "对 w 求导得到: $$X^{T}(Y-Xw)$$ 令其为0 解出w 如下$$w = (X^{T}X)^{-1}X^{T}y$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 标准回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[3.00774324],\n",
       "        [1.69532264]])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 导入数据\n",
    "def loadDataSet(fileName):\n",
    "    numFeat = len(open(fileName).readline().split('\\t')) - 1\n",
    "    dataMat = []; labelMat = []\n",
    "    fr = open(fileName)\n",
    "    for line in fr.readlines():\n",
    "        lineArr = []\n",
    "        curLine = line.strip().split('\\t')\n",
    "        for i in range(numFeat):\n",
    "            lineArr.append(float(curLine[i]))\n",
    "        dataMat.append(lineArr)\n",
    "        labelMat.append(float(curLine[-1]))\n",
    "    return dataMat, labelMat \n",
    "\n",
    "# 标准回归函数\n",
    "def standRegres(xArr, yArr):\n",
    "    xMat = mat(xArr); yMat=mat(yArr).T\n",
    "    xTx = xMat.T * xMat \n",
    "    if linalg.det(xTx) == 0:\n",
    "        print(\"The matrix is singular, cannot do inverse\")\n",
    "        return\n",
    "    ws = xTx.I * (xMat.T * yMat)\n",
    "    return ws \n",
    "\n",
    "xArr, yArr = loadDataSet('ex0.txt')\n",
    "ws = standRegres(xArr, yArr)\n",
    "ws"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xb94bdd8>]"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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5+oiJyDJVTQ+3L9Ie/bPABCCSJNkPgI+CntcXkWwRWSQiV5TSwFv9x2QX2NczYypHcjJkZrqg27cvjB8fvkedkOCCfEFB6WkV4PAxL4/8bx3jJq+j6NBR/vHOwzz9wdM0nzcLsrPB6z0x5RJI1yQlndhbD5fKCf4GYU5auYFeRC4F8lV1WQTHXg+kA08Fbe7gv8p8F3hWRM4KfZ2qvqSq6aqanpSUFHnrjTGRCwRQnw+WLIG5c8Pnv0PTKjt3lgy+Ph8Lszcw5tm5vDL/a67r34FP7jyf4YlxLsc/cGD4lEvw+w4fDp99VpzvV7WB18qkqmX+AI8DucBmYBdwCHgjzHGjcDn85DLe6zXg6rI+r1+/fmqMqQS7dqkmJKi6sFr8M3Soqs8X/jgR1fh4d4zXq98cPKL33viInnH3Bzr0jn/pgg35qsePq2ZmutdkZqp6PKper3uf0t43IcE9j2SfiQiQraXE1XJ79Kp6r6qmqGpHYDwwU1WvDz7Gn5d/ERirqvlB21uISD3/40RgELD25C9LxpiTFhjcDBYfD5Mnl0yNBA+Cqn6bgpm1ZAMXPD2HSck9+dGSqXz84o/JbHAMzjsPFi503w6WLnXVOOFSLuEGV8tK5ZioOek6ehF5WEQCVTRPAY2Bt0PKKLsB2SKyEpgFTFRVC/TGVDWfD/LzYeZM2L7d3RSVkOAGS0MHQYMrcIYMYV/jFtx1wyPc/N5GGjesxztr/sN98/5Jg4x+cPXV8Pnnxa/NyCg9SIeWZwana0JTOZaTj6qIqm6qklXdGBNloROVTZrkgvHu3eVWs/xv5XYe+O9q9h/x8tNhZ3H7iM7Ui5PigdrU1OKbqvr2dT36SCdBi7TyxkSkrKobmwLBmFgXfOPRvHkuOAfKHksJ8vkHjvDAe2v4eM0uerRvyj/H9SatXdPiA1q3Lp4XZ8EC15OfPz+yIB8omQyka2wpwEpngd6YWObxuJTNgAGwaJF7Hlz2GNKDVlWmfr6dhz9Yy+HjXiaM6cqtQzqREB8mgJ/MUn6h3y4++wz27LE6+Upmgd6YWOXxuPloCgvdXa5ffw3f/a4bOA3Tg96+/zC/mbqKOV8W0O+MFjwxrhedk8u517GiKz+FTmuwZ4+la6qABXpjYtW6dS7Ig/u9f78b6Azpgft8yr+XbGXi/77Ap/DgZWnckNmxchYEKW2hb1OpLNAbE6vS0lxPPtCjD0xpENSD3rz7IHe/k8Pir/cyqHMrJl7Vi9SWDSuvTSeT7jGnzAK9MbEqLs5V1oSZtyawIMgfZ6ynTnwcT4zryTXpqeFnmayMdlm6pkpZoDcmliUkQI8eJTZ9mXeAX0/JYeW2/YzqlswjV/SkTbP61dRAUxUs0BtTSxz3+vjb7K/4y8wNNKlfhz+N78PY3u2qphdvqpUFemNiVdAUv6u2f8Ovp6xk3a4DXNa7HQ9dlkarxvWqu4WmiligNyYW+evVjyxeyp++83+8lJpJq0Z1efmGdEanWX68trFAb0wsKigge/NeJnz/aTa1SuWabq247+q+NGtQp7pbZqqBLQ5uTCzx+Ti4bQcPLSrgO+Mf52hCPf61djJPXt/fgnwtZj16Y2KFz8f8K27invbD2N40mRszz+DX/frSKOUmq1ev5axHb0wMKDx8nLv/s5Tr066lruc4b03+DQ9lJtMotZ0FeWM9emNquhlr87j/vVXsLjrGbdsX8cspT1O/f7pNL2C+ZYHemBpqT9FRHnp/Le+v3ME5bZrwyg0Z9Gw3Bv7wM5tewJRggd6YGkZVeT9nJw9NW8OBI8e5c9TZ/GTYWdRN8GdibXoBE8ICvTE1SN43R7jv3dV8+kUevVOa8eTVA+japkl1N8uc5izQG1MDqCpvZW/jkQ+/4JjHx28uPodbBp0ZfkEQY0JYoDfmNLdt7yHunbqK+Rt30//MljwxrhdnJjaq7maZGiTi7oCIxIvIchH5IMy+eiIyWUQ2ishiEekYtO9e//b1InJhdJptTOzz+ZTXsr7mwmfnsnzrPn5/RQ8m/WiAC/I+n1tcW7W6m2lqgIr06O8AvgCahtn3A2CfqnYWkfHAE8C1IpIGjAe6A+2AT0XkbFX1nmK7jYlpXxUUcfeUHLK37OP8s5N47KqetG/ewO0MXXd11qzIFuU2tVZE/zpEJAW4BHillEMuB173P54CjBQ39+nlwCRVPaqqXwMbgf6n1mRjKlE195Q9/qmEL/rTPDbkF/GH7/TmtZszioM8nLjuakFBtbTV1ByRdgOeBSYAvlL2twe2AaiqBygEWgVv98v1bzPm9BPoKaekwLBh7nkV+mLnN1z5/AKe+HgdI7omM+OuoVzdL+XE+eITEyEjA+LjIT0dkpKqtJ2m5ik30IvIpUC+qi4r67Aw27SM7aGfcauIZItIdoH1Tkx1qaae8lGPl6c/Wc9lf5nPzsLDPP+9vrzw/X4kNwmz6pPPByNGwOLF0LAhZGe7i1MVX5RMzRJJj34QMFZENgOTgBEi8kbIMblAKoCIJADNgL3B2/1SgB2hH6CqL6lquqqmJ1nvxFSX5GSX805IcL+rYAqBFdv2c9lf5vPnmRu5rHc7Ztx5Phf3bFv6CwIXI58PDhyw9I2JSLmBXlXvVdUUVe2IG1idqarXhxw2DbjR//hq/zHq3z7eX5VzJtAFWBK11hsTTSJuYDM3F2bPDj+FQJRy+IePeXn0w7Vc9XwWB454+MdNGTxzbR9aNKob/gWBz01KgsxMN/jatGmVXpRMzXXSdfQi8jCQrarTgL8D/xKRjbie/HgAVV0jIm8BawEPcLtV3JjTWlxc6VMIRKnaZdGmPdzzTg6b9xziu+d14N6LzqFJ/TLmivf53JjBggUuyIu4z+3dGyZPhjZtbF4bUybR06wONz09XbOzs6u7GaY2Clpj9dvAGbwtP98N1Ho8riedm1t8UQj32hAHjhzniY/X8cairXRo2ZCJ43oy8KzE8tu1cye0a1f8PD4evN4T22BqNRFZpqrp4fZZ8a0xEL7iJnRbYmL4HH4E1Tqz1+dz4TNz+ffirfxg8Jl8/MshkQV5KJkmEnEVN5ayMRVgPXpjwOW/Q3vrcOK2pKQTe+47d0KHDmF7+vsPHePhD9Yy9fPtdE5uzJNX96JvhxaRtyuQtpk3zz0fMsSljHbvtqmITQll9ehtrhtjoLjiJpB/D/SUQ7eJlEyV+Hxw7bUuyIuUeO1Hq3by2/+uYf+hY/x8RGd+NqIz9RLiK9auggJYuNA9jo+Ht95yvy1dYyrAAr0xUFxxE9pbD7ctWHAgjouDyZMpKDrGg9NW879Vu+jerimv35JB93bNSr6urPGAxMTiHnvoBcgCvDkJlqM3tVdoqWSg4ibcQGxpKZKg2nsdNIip2z2MfmYOn67N59cXduW92weFD/JljQe0agXt27t9quWXfBpTDsvRm9qpvFLJ0P2ffQZ79oQP+j4fOzZt5zdzdzL7ywL6dmjOk1f3onNyKQuClDceEGBVNaYCrOrGmFDB0x1kZbnSyWB5eW4A1ONxv4cMCVtV4/Mp/166jQv+tZbFX+/lgUvTePu2gXRObFT6jVXh7sAN3tasmcvDW1WNiRIL9KZ2Sk52Nx9B8YBqcFmkSHGQVoWlS0+YbmDLnoN895VF3PfuanqlNGP6HYO5pUtD4rWccstwd+AGb9uzB7Zvt1SNiRoL9KZ2EnF3lSYkuEAeOl9M69auFx8fD4MHw6BB3/bAvYlJvDJvExc+O5c1279h4lU9+fdN/egw9gIX3IcMcd8SypqHJnQ8IHhboKrGgryJEqu6MbVXmzbhSyrBBdnZs4sHY1WhoIAN2oAJLy5k+db9jDwnmUeu7EHbJvXchWDRIvfapUvdTU3Z2WWnXyIZ7I3kGGPKYYHe1B6hQbO0ksqAoHlvjvuUF1Z/w19mfk6jevH8aXwfxvZu5+aKz8tzwT0gI8Pl9cu6qSmSeXNsJSkTJfavxtQOpU1TEC6FEmL19kIu/2sWf5zxJRd0b82Mu87n8j7tixcESU52Pfr4eBgwAObPL06/qBYPygaXc0Yy972tJGWixHr0JrYFevGBPHxw0CynbPHIcS9//mwDL87dRMtGdXnx+/24sHubEw8s7ZtBaI9c1d1cNXAgzJxZetoooLS7dY2pIKujN7GrrEA7e3ZxzzpMemXZlr1MmJLDVwUH+U6/FO6/JI1mDcuYSjic0Hr5wI1RZc2bE+4cLEdvImBz3ZjaKTT1sXWrS9UEBlfD5L8PHfPw5MfreX3hZto1a8A/b+nP0LNPctWz4B55o0ZQWOi2Z2aGnzcnnLLmxzcmQhboTewI7f2Gpj6CF+jIzz8hlZN1IJ57puawbe9hbsg8gwljzqFxvVP4LxJI6axdC336uG0JCW5iMuudmypkg7EmNoQbbC1racCgO1G/GTKMe+bn8b1XFpMQF8dbP87k4ct7nFqQD4iLg27dXCVO4G5X66GbKmY9ehMbwlWotG5deurDfxH4dNEG7pu9jYLsbfz4/E7cOeps6tep4FTCZfH5YMQIV1Pfv78bhLXevKliFuhNbAhO02Rmuhy8aqlBde/BY/zu/TX8d8UOzmnThJdvSKdXSvPotyv4ArR0qauttx69qWKWujGxIZCm2brVPU5NDTvPjKry/sodjH56Dv9btZNfjurCtJ8NrpwgD+EnMDOmilmP3sSOuDj3U0q9fN43R7j/vdXMWJtHr5Rm/Pvq8zinTdPKbVN5d98aUwXKDfQiUh+YC9TzHz9FVR8MOeYZYLj/aUMgWVWb+/d5gVX+fVtVdWyU2m7MicLcZKSqvL0sl99/sJZjHh/3XnQOPxh8JgnxVfSF1kokTTWLpEd/FBihqkUiUgeYLyIfqeqiwAGqemfgsYj8HDg36PWHVbVP1FpsTFmCe9CJieRu3Ma9c3cyb8Nu+ndsycRxPemU1Li6W2lMlSo30Ku7dbbI/7SO/6es22mvAx4sY78xlSsuDl+rRN647v+YmDIYiY/n91f24XsDOhIXZ6kTU/tE9N1VROJFZAWQD8xQ1cWlHHcGcCYwM2hzfRHJFpFFInLFKbfYmNJ4PLB6NZvyDzD+b/N5oNNo+m3/gul/v53vn9XQgryptSIajFVVL9BHRJoD74pID1VdHebQ8bgcvjdoWwdV3SEinYCZIrJKVb8KfpGI3ArcCtChQ4eTOhFTy3k8eBKTeKXrSJ4Z8j3qNW7IUxv/x9X/fQmxahdTy1VoNEpV9wOzgTGlHDIeeDPkNTv8vzf5X3tu6ItU9SVVTVfV9KSkk5xXxNRq6xas4KrLH2Di8JsZ9lU2n16UzHfe+gsS7q5YY2qZcgO9iCT5e/KISANgFLAuzHFdgRbAwqBtLUSknv9xIjAIWBudphsDxzw+npnxJZd9nM/2psk8997jvPDeYyR3aBPRXPPG1AaRpG7aAq+LSDzuwvCWqn4gIg8D2ao6zX/cdcAkLTnvcTfgRRHx+V87UVUt0JuoWLltPxOm5LA+7wBX9GnHAy/9iZYbF7k1W9uEmTfemFrK5qM3Nc6R416envElr8zbRHKTejw2PJURA84uc355Y2JdWfPR2xQIpkZZvGkPY56dy0tzN3FteiqffPoEI4b2cNMdgKVqjAnDpkAwNULRUQ9PfLSOfy3aQmqLBvxn3NkMTG0C42dXaHlAY2oj69Gb096cLwu48Jm5vLF4C7cM6sj0jx9j4MA0uOYamzDMmAhYj96ctvYfOsbvP/iCdz7PpXNyY6bcNpB+9Y/B/DmuF79wYcnlAS1lY0xYFujNaenj1bv47X9Xs/fgMX42vDM/G9HZLQiiWvrygMaYsCzQm9NKwYGjPDRtDR+u2kla26b846YMerRv5uaVz8tzPXeb9teYCrFAb04Lqsp/V+zgoffXcOiol19dcDY/Pv8s6sTHFa8HG+jFz5plg67GVIAFelM6n69Kes47Cw9z37urmbkun3M7NOfJcb3o0rpJ8QGlrQdrjImIVd2YkgIpEq/X9aJTUsIuyRcNqsqbS7ZywdNzWfDVbn57aRpTbhtYMsgDJCZCRoZV1xhzkqxHb4oFp0jS0yE7u9J60Vv3HOKeqTks+GoPmZ1aMXFcT85o1Sh8m0aMgCVLXLCfOdPy8sZUkAV6Uyw4RXYHwC4AABe/SURBVLJ0KfTv735HsRft9SmvLdjMH6avJz5OeOzKnlzXPxUpLXgH2uT1ugvP7t2WtjGmgizQm2KB9Vazslzvee5c2LMnajn6jfkHmDAlh8+37mfEOck8emUP2jZrEFmbgtaANcZUjAX62ircQKsIfPYZDB3qevIjR7oKl3BBvgIDtce9Pl6au4k/fbqBhvXiefbaPlzep13pvfhgwWvAWjmlMSfFBmNro0AuPnSg1eeDdetcPjw4Nx/8ugoO1K7eXsjlf83iqenrGZ3Wmhl3ns8V57aPLMgbY6LCAn1tFK5cMRD8zz0XGjeG+PiSqZLgi8OQIS69E+5i4HfkuJenpq/j8ueyKCg6ygvX9+O57/UlqUm94vfLy3N3uoYK3lfaRckYEzEL9LVRIO8dXK4YHPwPHoQVK0ouwRc6UFtGueOyLfu45M/zeG7WV1x5bns+/eUQxiRJcVAvK3gH9rVr5yp/du488aJkjKkQC/S1USDvnZvryhXz8yEpqWTwT0ws+ZrQi8PcubB8eYkc/qFjHh5+fy1Xv7CAI8e9vH5lF/5wVQ+aXXxByaAe7htFQEEBzJ/vjvv8c+jWDQYMsBp6Y06BBfraKi7OBfcRI1wQHj7cDcRu3ep63qmpJXvbqjBpEmzb5i4Oo0a5NM/w4eDzsWDjbsY8O49Xs77m+v4dmD59IucP7g6DB58Y1MN9owhIToY+fYqfHzgAzz3nLkq2yLcxJ8WWEqzN8vJckPd4XNDNzXXbQ7clJZWca2bSJOjQATwevmnYlMdf/IQ3V++mY6uGPDGuF+c18hS/R3x8yXr8QLAuq2rH44GWLV2Qb9YM9u51FyZjTKnKWkrQyitrK5/P9dIzM9287sE969C69fz8kr1yERg4kM92HeO+i+8gf81ufjy0E3eOPjv8VMIzZ7obnYKDelxc+BuffD5Xu79nD6xfD2lpFuSNOUUW6Gsjj6e4Vn7gQJeuCZ7XPbRuPeSmpX2NW/C7nzzLeyt20LV1Y168uje9U5sXv3+42vdI7mYNN0ulBXljTlm5/4tEpL6ILBGRlSKyRkR+F+aYm0SkQERW+H9+GLTvRhHZ4P+5MdonYCrI53PlkQsXFvfQ4+JKpk8Cve3gG6lmzUK3bePDv7zJ6Gfn8kHOTu4Y2YX3bx9E77pHw5dJlteO0PLKsgZpjTEnLZLu0lFghKr2BvoAY0RkQJjjJqtqH//PKwAi0hJ4EDgP6A88KCItotR2czIKCtwNUQEZGRFVsuQXHeO2Gbnc/p/ltG3WgPd/Ppg7R3am7uiR4W+8Gj4c2rd37+/xlHwzjwcGDXL7g19X1iCtMeaklZu6UTdaW+R/Wsf/E2n37UJghqruBRCRGcAY4M2KN9VERWIiNGkChYXQqBHMmXPiYGjQQKkCU5bl8vsP1nLE4+Oei87hh4PPJCE+zvXIw80TX1DgbqjyemHZMmjRAvbtcwHc53Npo0WL3GfNnw9r10L37jbdgTGVJKIEqIjEi8gKIB8XuBeHOWyciOSIyBQRSfVvaw9sCzom178t9P1vFZFsEckusK/r0RWaItm9290QBe730KHhb1hKSWH7BZdx46tL+PWUHLq2acLHdwzhtvPPckEeSu+BJydD797F71lU5II5uCC+dGnxvkaNXJlmoGcfmjYyxpyyiAK9qnpVtQ+QAvQXkR4hh7wPdFTVXsCnwOv+7eH+t57wbUBVX1LVdFVNT0pKirz1pnQ+n7urdNiw4tSKx+MCfnpQBdbSpSfcsORbsJB/9byAC3reRPbmvfxubHcm35pJp6TGJT8j+Mar4Bp3EXjvvZLHtmrlfgdfHPr1g0OHLCdvTCWrUEmDqu4HZuPSL8Hb96jqUf/Tl4F+/se5QGrQoSnAjpNqqYlcoFfeoQPMm1ccSIcMcTdCJSS4u03j412uPCgX/nVcI8b/6M/89oKf0vfQLqbfOZQbB3YkLq6UHnZpPfA6dUo+j493v4MvDkuWuM+3nLwxlarcHL2IJAHHVXW/iDQARgFPhBzTVlV3+p+OBb7wP54OPBY0AHsBcG9UWm5KF1y9IuKCcUaGC6xer8uPb93qtvtz4R6vj1ezvuaPn3xJveQzeXJoCt8ZdhFysuWNrVu7C0ugVDK4vDK4ht5y8sZUukjq6NsCr4tIPO4bwFuq+oGIPAxkq+o04BciMhbwAHuBmwBUda+I/B4IJGUfDgzMmkoUXPeememmEEhLc9MdBAJvUN38+l0HmDBlJStzCxmd1ppHruhB66b1T60NIi6dU14QL+3GKWNM1NgUCLEqMAg7fnxxcP/ssxIrRh3z+Hh+9kaem7WRpvXr8NDY7lzaq2105oqvwMIkxphTZ1Mg1FZ79pQsf9yz59vec07ufiZMyWHdrgNc3qcdD17WnZaN6kbnc+0OV2NOKxboY1Eg0GZluUVEDh78drDzyHEvz3z6JS/P3URSk3q8ckM6o9KinDoJd4erpWeMqTYW6GNRINB6va6GfcUK6N6dJZv3cfc7OXy9+yDjM1K59+JuNGtQp/z3qyhb0NuY04oF+lgUEmiLOnflyWlr+OfCLaS2bMC/f3gegzonlv8+J8vucDXmtGKBPtYEBkH9UwPPKxTueXYeOwoPc/Ogjvz6wq40rFsFf+1WTWPMacMCfSwJGgQtHDKcR37yJG8v206npEZMuS2Tfme0rO4WGmOqgQX6WOLPzX/SsR/3p32fPZ9v56fDzuIXI7u4BUGMMbWSBfpY4fOx5+AxHrzxcT5I7Ea3g3m8evsgeqQ0L/+1xpiYZoE+BqjXy7RrbuehlPM52LILv8psy48vGUOdBOvFG2MqOKmZOf3sKjzCD19ZwB1dLuOMfTv48PVf8rMB7S3IG2O+ZT36GkpVmbx0G49++AXHDx3m/jmvc/Oy94kfPMjq1o0xJVigr4G27T3EPVNzyNq4hwEpTZj4ux/ScXeumwp48mSrWzfGlGCBvgbx+pTXF2zmqenriY+DR0eewXXDuxH3didYsOvE6YCNMQYL9DXGxvwi7n4nh2Vb9jG8axKP/udh2j02PeyslMYYE8wC/WnuuNfHS3M38afPNtCwbjxPX9ObK9slILdODzsrpTHGhLJAfxpbs6OQCVNyWLPjGy7u2Ybfje1BUpN6bt1XmzTMGBMhC/SnoaMeL3/5bCMvzPmK5g3r8sL1fRnTo23xAaowaZJL04Rbr9UYY4JYoD/NfL51H3dPyWFDfhFX9W3PA5em0bxh0IIg4Rb1sEBvjCmDBfrTxOFjXv7wyXpezfqatk3r84+bMxjeNUxKxhb1MMZUkAX608CCr3Zzzzur2Lr3ENcP6MDdY86hSf1SFgRJTIT0dFi61PLzxpiIlBvoRaQ+MBeo5z9+iqo+GHLMXcAPAQ9QANyiqlv8+7zAKv+hW1V1bPSaX7MdOHKcxz9ax38Wb6Vjq4ZMunUAAzq1Kv0FPh+MGAGLF7s8vc/nflvqxhhThkh69EeBEapaJCJ1gPki8pGqLgo6ZjmQrqqHROQnwJPAtf59h1W1T3SbXfPNWpfPb95dRd43R/jRkDO5a3RXGtQtZ36aQNpG1T1fuNBSN8aYcpU7qZk6Rf6ndfw/GnLMLFU95H+6CEiJaitjyL6Dx7hr8gpufm0pTeonMPWng7jvkrTwQd7ng7y84sAeWCIw0IO31I0xJgIR5ehFJB5YBnQGnlPVxWUc/gPgo6Dn9UUkG5fWmaiq751sY2u6/63ayQP/Xc3+Q8f5xcgu3D78LOqVNstkaHVN4O7XmTMhP99KK40xEYso0KuqF+gjIs2Bd0Wkh6quDj1ORK4H0oHzgzZ3UNUdItIJmCkiq1T1q5DX3QrcCtChQ4eTPJUoCay5GsXpBPIPHOGB99bw8Zpd9GjflH/ech5p7ZqW/aLQ6pohQyA7u7ikMs5mmDbGRKZC0UJV9wOzgTGh+0RkFHAfMFZVjwa9Zof/9yb/a88N874vqWq6qqYnJSVVpEnR5fPBsGHQvj2cf757HtgenEKJ8L101y7eWbaN0U/PZeb6fO4ecw7v/XRQ+UEeitM0CQmQkeGqbIJLKo0xJkLlBnoRSfL35BGRBsAoYF3IMecCL+KCfH7Q9hYiUs//OBEYBKyNXvOjLC8P5s0Dr9f93rWrOIWSkuIuAoHgXxafj+0XjuWmO17i/97OoUtyYz66Ywg/GXYWCfERXltFXM89Nxfmz4dBg1zQt7y8MaaCIkndtAVe9+fp44C3VPUDEXkYyFbVacBTQGPgbXHpjkAZZTfgRRHx+V87UVVP30AfmqoZOxamTYv8BiWfD19+Pv9eWcDEnjehwEMzX+aGaS8Ql9Q48nYEp48CnzVrVtRTSsaY2kG0IumIKpCenq7Z2dnV8+GqkJnp6tQDzjsP6tZ1pYwDB8Ls2eEDrc/H5ouu5O7EgSxO7cHg/Zt5/O3HSO3RufTXBL322yCu6r5BZGW5lM0770DbthbcjTFlEpFlqpoedp8FekoG2u3bITW1eF98PGzb5gY/S+lNe33Kqx/n8MfPvqKO9zj3z3mNaz78OxIfX3YPPJD7Hz++uLpm0iT3+V5v8XFDhriLhQ3AGmNKUVagr71TIASCe2Kiu9s0EGhDc/CDBkGbNqUG6y/zDvDrt1eyMreQUQe28uhbj9G6d7eye+HBAT4rq/gO18DNUL17w+efFx9vc9oYY05B7Qz0wTXq6emubDGQg/d4io9bsQJ69QobsI95fPxt9lf8ddYGmhw5yJ+nP89lrXzIFyvLvDB8+9nBAR7cQGtmJowbBzk50KQJHDjg9tkArDHmFNS+XIDPB2vXFgf1pUtdLjwhwQX9YElJYQP2qtxCxv51Ps98+iUXdW7BjJdvY+ya2UhgtaeyBOrjvV4X5BMSXGpmyxY4dgwWLXLtOnwYVq6EnTthzhzL0RtjTlrtCfQ+nwuaw4dDnz7QqJELsoMGuVLK3FyYOrXka0Jy4keOe5n40TqueD6LvQeP8fIN6fz5hv606tHVvVejRu69yyrDDK6PHzLE5f/nzHFjAcFjExkZ0LNn2d8OjDEmArUjdRMuXVJU5FIz3bsXTyeg6oJvIF8flBPP3ryXCe/ksKngINemp/KbS7rRrF68e98lS1yAX77cvX+4nHrwgG+4UsnkZHfRCVTbzJ9vAd4YExW1I9AHp0vA9Z4zMiAtrWQwFXHVLUFB+OBRD09NX8/rCzfTvnkD3vjBeQzukuiOz8srft+VK6F//+JpCoJz6uFWhUpKcjdkBc9ZY7XyxphKUDtSN8HpksGDXZDPznbBNzTFEhf3beCdv2E3Fz47l9cXbubGzI5M/+XQ4iAf+r6BGvsZM9zEY4FAHRgTyMoqHvDNy3Of3b69q84JTLcQ9NnGGBMttaNHH9xbVnV16mXc6Vp4+DiPffgFk7O30SmpEW//OJP0ji3Lft+WLV0vvbAQmjWD3btd4A705Bs3dumigQNdG7KyiiturHzSGFOJakegh+LesqoLtoE0SkjZ4oy1edz/3ip2Fx3jJ8PO4o6RXahfp4wFQQLvu3q1C/Lgfq9d6/YFqnsOHnRjAt26ueAffEOUlU8aYypR7Qn0UDwgOnOm63EH5cL3FB3loffX8v7KHZzTpgmv3JBBz5Rmkb93WprryQd69Lff7qZNaNzYBfmBA93Ab36+2w7uQrBiBfToYekaY0ylqT2BPtyAqAiqyvs5O3lo2hoOHDnOXaPP5rbzz6JuQgWHL+Li3MVj3Tpo1Qo6dHC99sJCt0/V/QTy+oF2WJA3xlSy2jPXTV6em2rY43GDp7m55DVoxn3vrubTL/LondqcJ8f1omubJqf+Waqulj74Tlv/Z9K6daUsbmKMqd3Kmusm9qpuSlskJKhCRgcOZPKWo4x6eg7zNhRw38XdmPqTgdEJ8lA8SLttm6vLD51H3qprjDFVKLZSN4EVogJpkeAZH/3Bd9vGXO6du4P5U1dx3pkteWJcLzomNop+W+Li3F2tIXX5xhhT1WIr0AdWiAL3Oy/P1akDPp/yz4VbeHL6egR45IoefLd/B+LiKjn4BnrvxhhTTWIr0Iu4H9Xix8BXBUXcPSWH7C37OP/sJB67qiftmzeo5sYaY0zViK1A37p1iblqPIlJvDR7I89+uoEGdeL543d6c1Xf9oilUIwxtUhsBfqgO1XXeusz4W8LWL39Gy7q0YbfXd6d5Cb1q7uFxhhT5WIr0ANHfcpzK/fz/OyvaN6wDs9/ry8X92xb3c0yxphqE1OBfsf+w9z0jyV8mVfEVee257eXptGiUd3qbpYxxlSrcuvoRaS+iCwRkZUiskZEfhfmmHoiMllENorIYhHpGLTvXv/29SJyYXSbX1JSk3qc0aoR/7gpg6ev7WNB3hhjiKxHfxQYoapFIlIHmC8iH6nqoqBjfgDsU9XOIjIeeAK4VkTSgPFAd6Ad8KmInK2q3tAPiYY68XG8fEPYG8OMMabWKrdHr06R/2kd/0/ovAmXA6/7H08BRoorbbkcmKSqR1X1a2Aj0D8qLTfGGBORiKZAEJF4EVkB5AMzVHVxyCHtgW0AquoBCoFWwdv9cv3bjDHGVJGIAr2qelW1D5AC9BeRHiGHhCtM1zK2l3yxyK0iki0i2QUFBZE0yRhjTIQqNKmZqu4HZgNjQnblAqkAIpIANAP2Bm/3SwF2hHnfl1Q1XVXTk5KSKtIkY4wx5Yik6iZJRJr7HzcARgHrQg6bBtzof3w1MFPd/MfTgPH+qpwzgS7Akmg13hhjTPkiqbppC7wuIvG4C8NbqvqBiDwMZKvqNODvwL9EZCOuJz8eQFXXiMhbwFrAA9xeWRU3xhhjwqs9C48YY0wMq10LjxhjjCnhtOvRi0gBsKUCL0kEdldSc05ntfG8a+M5g513bXIq53yGqoatZjntAn1FiUh2aV9XYlltPO/aeM5g513d7ahKlXXOlroxxpgYZ4HeGGNiXCwE+pequwHVpDaed208Z7Dzrk0q5ZxrfI7eGGNM2WKhR2+MMaYMNSbQi8gY/+IlG0XknjD7S138pKaK4JzvEpG1IpIjIp+JyBnV0c5oK++8g467WkRURGKiMiOS8xaRa/x/52tE5D9V3cZoi+DfeAcRmSUiy/3/zi+ujnZGm4i8KiL5IrK6lP0iIn/2/7nkiEjfU/pAVT3tf4B44CugE1AXWAmkhRzzU+AF/+PxwOTqbncVnPNwoKH/8U9q+jlHet7+45oAc4FFQHp1t7uK/r67AMuBFv7nydXd7io455eAn/gfpwGbq7vdUTr3oUBfYHUp+y8GPsLNADwAWHwqn1dTevT9gY2quklVjwGTcIuaBCtt8ZOaqtxzVtVZqnrI/3QRbnbQmi6Sv2uA3wNPAkeqsnGVKJLz/hHwnKruA1DV/CpuY7RFcs4KNPU/bkaY2W9rIlWdi5sXrDSXA/9UZxHQXETanuzn1ZRAH8kCJqUtflJTVXTRlh/gegA1XbnnLSLnAqmq+kFVNqySRfL3fTZwtohkicgiEQmdLrymieScHwKuF5Fc4H/Az6umadUuqos2RTJ75ekgkgVMIlrkpAaJ+HxE5HogHTi/UltUNco8bxGJA54BbqqqBlWRSP6+E3Dpm2G4b2/zRKSHunUiaqJIzvk64DVV/aOIZOJmye2hqr7Kb161imo8qyk9+kgWMClt8ZOaKqJFW0RkFHAfMFZVj1ZR2ypTeefdBOgBzBaRzbj85bQYGJCN9N/4f1X1uLo1mNfjAn9NFck5/wB4C0BVFwL1cfPBxLqI/v9HqqYE+qVAFxE5U0Tq4gZbp4UcU9riJzVVuefsT2G8iAvyNT1fG1DmeatqoaomqmpHVe2IG5sYq6o1fW7rSP6Nv4cbgEdEEnGpnE1V2sroiuSctwIjAUSkGy7Q14b1RqcBN/irbwYAhaq682TfrEakblTVIyI/A6bjRupfVbeoSbmLn9RUEZ7zU0Bj4G3/uPNWVR1bbY2OggjPO+ZEeN7TgQtEZC3gBX6tqnuqr9WnJsJz/j/gZRG5E5e6uKmGd+AAEJE3cSm4RP/4w4NAHQBVfQE3HnExsBE4BNx8Sp8XA39mxhhjylBTUjfGGGNOkgV6Y4yJcRbojTEmxlmgN8aYGGeB3hhjYpwFemOMiXEW6I0xJsZZoDfGmBj3/94Zaxc9Jzz1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘图\n",
    "import matplotlib.pyplot as plt \n",
    "\n",
    "xMat = mat(xArr); yMat = mat(yArr)\n",
    "yHat = xMat * ws\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.scatter(xMat[:,1].flatten().A[0], yMat.T[:,0].flatten().A[0], s=5, c='red')\n",
    "\n",
    "xCopy = xMat.copy()\n",
    "xCopy.sort(0)\n",
    "yHat = xCopy * ws \n",
    "ax.plot(xCopy[:,1], yHat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.98647356],\n",
       "       [0.98647356, 1.        ]])"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 判断模型好坏\n",
    "# 计算预测值 yHat 与真实值 y之间的相关系数\n",
    "corrcoef((xMat*ws).T, yMat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 局部加权线性回归 LWLR （ Locally Weighted Linear Regression）\n",
    "线性回归可能出现欠拟合现象，因为它求的是最小均方误差的无偏估计。\n",
    "\n",
    "在预测点附近的每个点赋予一定的权重，回归系数形式：$$ w = (X^{T}WX)^{-1}X^{T}Wy $$ \n",
    "LWLR 使用“核”（与支持向量机中的核类似）来对附近点赋予更高的权重，常用高斯核，高斯核对应权重如下：\n",
    "$$w(i,i) = exp\\left(\\frac{|x^{(i)}-x|}{-2k^{2}}\\right)$$\n",
    "这样构建了一个只含对角元素的权重矩阵 w，且x 与 x(i) 越近，w(i,i)越大"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lwlr(testpoint, xArr, yArr, k=1.0):\n",
    "    xMat = mat(xArr); yMat = mat(yArr).T\n",
    "    m = shape(xMat)[0]\n",
    "    weights = mat(eye((m)))\n",
    "    for j in range(m):\n",
    "        diffMat = testpoint - xMat[j, :]\n",
    "        weights[j, j] = exp(diffMat * diffMat.T / (-2.0*k**2))\n",
    "    xTx = xMat.T * (weights * xMat)\n",
    "    if linalg.det(xTx) == 0:\n",
    "        print(\"The matrix is singular, cannot do inverse\")\n",
    "        return \n",
    "    ws = xTx.I*xMat.T*weights*yMat\n",
    "    return testpoint * ws\n",
    "\n",
    "def lwlrTest(testArr, xArr, yArr, k=1.0):\n",
    "    m = shape(testArr)[0]\n",
    "    yHat = zeros(m)\n",
    "    for i in range(m):\n",
    "        yHat[i] = lwlr(testArr[i], xArr, yArr, k)\n",
    "    return yHat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[3.12204471]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0xbc57b38>"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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kpkzhhV7ns+BwC+5J6cfIkbP8HZH1zf2g3uPQReQBnOEz83BaLK2AN123kNqpqmO9E6IxpjbrU2cwY2c7ftTiCLeO6O3vcByeXGw1XlWnhK6q6UC66/G0Kq+P8mpUxhiPlZZXMKmiD7GtS3jkzgvsvpxNmM0UNSbIPffFVtZ/d4hnfzWUuFYnGZ5oQp7dsciYILbtwGH+8tEmLhvYieQBnfwdjvEzS+jGBClVZfLcVURFhJE2doC/wzEBwBK6MUHqjaxdLN36PVP6NaPDVT+x8d7GeujGBKPsgmIe+u96zunVjl/MtnVSjMMSujFBKG3eOorLKnh43BmEnWnjvY3DEroxQWbR3M/47+pC7jqtOb3jW0G8jfc2DuuhGxNECopLmbp4H6dlb2PC64/7OxwTYCyhGxNEHvtgI/ubteLhvK9oNm2qv8MxAcZaLsYEieU7vuflpTu4YXgCgx+Z7e9wTACyCt2YIFBSVs69b6+mS+vm3HVpP3+HYwKUVejGBIFn0rewObuQF288m5ZR9s/WuGcVujEBbtP+Ap76dDNjB3Xhon4d/B2OCWCW0I0JYBUVyh/nrqZlVATTxvT3dzgmwFlCNyaAvbx0B8t3HOT+K/rT3lZSNLXwOKGLSLiIrBCRBW62RYnI6yKyWUQyRSTBm0Ea0xRtW7SYR975hgs7RPKzIV39HY4JAnWp0P8ArK9h23jgoKqeCswEHm1oYMY0ZSVl5dw+fxPNjhbz6KfP2k0rjEc8Sugi0g24Ani+hl1+DFQOjH0LuETsb6Ax9fbI+xtY06IDM/Z9Tucpd/k7HBMkPK3Q/wLcA1TUsL0rsAtAVcuAfCCu+k4iMkFEskQkKycnpx7hGuMlGRmQkhKQS85+sHYfL365nRtOiSJ5x9cwcWJAxmkCT60JXURGA9mquvxku7l5TU94QXWWqiaqamJ8fHwdwjTGy9JcS86mpfk7kuPsyTvCPW+tYmDXWCa/8yRkZjpfARanCUyezFAYDowVkcuBaCBWRF5R1euq7LMb6A7sFpEIoDXwvdejNcZbUgNvydmio2Xc+spyyiuUf1w9hKjEqXDQ9c8ogOI0gavWCl1VJ6tqN1VNAH4JfFItmQPMA653Pb7Stc8JFboxASPJteRsUpL77Y3ckikrr+D3c1awZnc+f1n/DgmbVjkb2rSBmTNrjtOYKuo9h1hEHgCyVHUe8ALwsohsxqnMf+ml+Izxj7TGuwuQqjL1vbV8siGbBxe/xKgv34JD252NdiciUwd1Suiqmg6kux5Pq/J6MfBzbwZmjM9kZDgJOzW15srXXUvGk/fVUUWF8uB/1/OfZTu5bX8W1335FsTFHf+51m4xHrJVfkzTU736dpeok9zcBcjLVXtZeQWT567mzeW7ueG8BO5q3xa+yzg+DqvMTR1YQjdNT/Xq29NE7cULqQXFpfzfGyv5cN1+/nBJH+4c1QdZurTBxzVNmyV00/RUr74becTLt/sL+O0ry9mRW0TqmP7cOLyXs6ER+/YmNFlCN8Zde8WdBibcwpIynknfzHNfbCM2OpJXk1px7p9vPdZiCcChlCa4WEI3JiMDTUsj949T2XvqAErKKoiKCKNnu5a0bhF5bL/6JNyMDMrTHuDNG+7h8c3lHCgs4SfdmjFl4dN0WLDXmTQEx4ZQWmVuGsASugl9NYxOKS4t56P1+3nnhaUsHjCBkoV5wJfHvbVb2+YM7NKaAV1iGdi1NwPeeJcOsdEefWxOQQmf/P1NZne+jHXfFDGkRxue+/VQBk+42qn0hw2D5GSryI3XWEI3oa+yVZKVBfPnkz1wMDMXbWLByr0UlJTRKaYTV6/8gITWzegSXkbzr5Zy5Oxz2XLbXazZm8+6vYdYuHbfD4dr3yqK/l1i6d85ltMK9tH2zTm0vP46IgedyYHCEtZ/d4iP1mezcnce2uMSepTk8/fEloz+2XnOqolVK32bMGS8yBK6CX2pqZCVhebm8t7f/kPqaQUcKS1nzJldGDekK+dmf0v4+h1wV+Wol20w8deQ1PuHQxQUl7L+uwLW7s1nzZ5DrP/uEC9s2UppuULvH8PiAlh8rLo/s1trJo7qyyWnd6B/59jjl7+11orxEfHXDP3ExETNysryy2ebpif70y+5742vWdT6FAb3aMNjVw7i1A6t6ncwVwvn6NRp7Cis4NCzz1N0/U2U9OlH+5gourdtTpzdXcj4iIgsV9VEd9usQjchL2v790xYXERh3KlMubQv488/hfCwei7Xn5EBY8ZAbi7NgD4LF0Ly+Q0L0AczUE3TZPcUNaGl2qJan27M5prnMmndPJL/3XE+Ey7sXf9kDk7izc09cXq+h/HUeMwAXMrXBB+r0E1oqTJW/Iu/v8wtLy+nb6dWvDJ+GG1aNGv48Wu6oFlZZY8bB3PnHtvuydh1G39uvMQSugkNVRMqsOS2Kfxmdha9472YzKHmC5pVR9Lk5jqvLVzoWbK2i6TGSyyhm9BQpRJe9swcxv9rGT3jWvDKoDDajBvr+/50ZcKuWqGDJWvTqCyhm9DgSqBf334fN764jC5tonn1N+cS9/MfN876KJVT9+3ipvEjT+4pGi0iy0RkpYisFZETrtyISA8R+VREVojIKtft6ozxDXcXGpOS2DVnLjd/XUz7mCjm3Hwu8TFRTnJtrNmYdnHT+JknFXoJcLGqFopIJLBYRN5X1aprfd4PvKGqz4hIf+B/QIL3wzUGtxcaC0vK+M3sLI6WV/CvG86mY+X0/MZqeWRkQF6eM53fLm4aP6k1obvuDVroehrp+qo+G0mBWNfj1sBebwVozAmqXWhUVSa9/g2bcwp56caz6R1fzwlDDZGW5iy0lZxs7RbjNx710EUkHFgOnAo8paqZ1Xb5E/ChiNwOtARG1XCcCcAEgB49etQzZNPkVau6n/tiKx+u28/U0f25oE+8f2KyoYcmANRp6r+ItAHeAW5X1TVVXp/kOtYTIpKEc9PogapaUdOxbOq/abCMDJY9/hxX9/0Zlw7oxNPXDjl+zRRjQtDJpv7Xaaaoqubh3CQ6pdqm8cAbrn0ygGigfZ0jNaYOch6awe87jaTHkYPMuPJMS+amyfNklEu8qzJHRJrjtFM2VNttJ3CJa5/TcRJ6jndDNeaY8grlzpG/Jb9la55O6UlMdGTtbzImxHnSQ+8MzHb10cNwRrMsEJEHgCxVnQf8H/CciEzEuUB6g/prGUfTJDz3xVa+PFDGoz8fzOln2/UYY8CzUS6rgMFuXp9W5fE6YLh3QzPGvTV78nniw41cNrATVyV2t9UKjXGxmaImqBQvXsKdr39Lu4gopndv7fTNG3jzZmNChSV0E1QefjGdzfGDePn1+2m7viOM8HABLGOaAEvoJmh8ujGb2fGDuGnV+1zQ4qgtgGVMNXaDCxMUcgtLuOetVfQ9kss9H86C7t2tX25MNVahm4Cnqkyeu5r8olJmX9aL6I0XW3vFGDcsoZuA9/pXu/hw3X7uu/x0+l94CqRYe8UYd6zlYgLa5uxC0t5bzfCCXYyP2OfvcIwJaFahm4BVUlbOHf9ZQXTJEZ78932EbTnbLn4acxKW0E3AeuzFdNZ9V8zzXYvoOPxs65sbUwtL6CYgpW/M5vktxfx6+QJGhW+zytwYD1hCNwEnp6CEu95cSb+YcKZE7IRpVpkb4wlL6CagVFQod725koLiMl79/flE31d9pWZjTE0soZuA8uKcdD77tog/n9mCfp1i/B2OMUHFhi2agLFqdx6Pripg1KalXPfvR/0djjFBxxK6cZafTUlxvvvJ/kPF3PzvLOJbRjKjeDViI1qMqTNL6E1R9QReufxsWppfwikuLWfCv7MoOFzC8yteod3999o6LcbUQ609dBGJBj4Holz7v6WqJ5RPInIV8CecOxatVNVrvBuq8Zrq64f7cflZVeXet1excnc+z277L6e/NweKc22YojH14MlF0RLgYlUtFJFIYLGIvK+qSyt3EJE+wGRguKoeFJEOPorXeEP1BO7H5WefTt/Ce9/s5e7kfiRHt4P8rTaByJh6qrXloo5C19NI11f1+4XeDDylqgdd78n2apTGu5KSnKSZlubXvvl/lu3ksQ828pOzunDbyN7HfrFYu8WYevGohy4i4SLyDZANLFLVzGq79AX6isiXIrJURNwOHhaRCSKSJSJZOTk5DYvcNIynfXMfXTB9Z8Vupryzmov6xTPjykHOreSMMQ3iUUJX1XJVPQvoBpwjIgOr7RIB9AFGAlcDz4tIGzfHmaWqiaqaGB8f37DIjWfcJeSMDMjLg2HDTmxv+PiCqaryj082MfH1lQzr1Y6nrx1Ks4iwgBhpY0ywq9PEIlXNE5F0IAVYU2XTbmCpqpYC20RkI06C/8pbgZp6cncD5bQ0yMyE5OQT2xs+vGB6tKyCyXNX8/bXu/nJWV149MoziYoIrzlOY0yd1Fqhi0h8ZbUtIs2BUcCGaru9C1zk2qc9Tgtmq3dDNfWSmuok7qoJ2d1rNW2rS1+7epVd5Xle0VF+/a9M3v56N3eO6sPMHkeIGn0FzJrl7DNuXM0xGWM8o6on/QLOBFYAq3Cq8mmu1x8AxroeC/AksA5YDfyytuMOHTpUTSNaskQ1Odn57s33VN0nOVkVnO+qPzxf/+Nr9KLHP9U+U/6nc7/eddw2jY11vg8bVv9zM6YJAbK0hrxaa8tFVVcBg928Pq3KYwUmub5MIKre0sjIQNPSOHDvVLYlnE7R0TLCw4Tw9etp9eLz9LjzFto8/Ofa2yBVj1utPfP9H6fybOfzeKHTUGKLSnnlN8M4p1e74/fdtQvWrfPBCRvT9IiTixtfYmKiZmVl+eWzm6SMDCf5pqayrFM/Xn34JT6P7sTBFq1rfEtspNAzfx/9+nXn9EGn0ju+JQlxLenatjmR4WEnHJekJIpLy/lo/X7eXbGH9I05lFUoVyV2Y/Jlp9O2ZbOTxmXDFY2pnYgsV9VEt9ssoYewasly474CZizcwMcbsmnbTLho3zrOuHAovc4eQGzzSCoqlLLVa8h/5TV2jb6SHTEd2J57mPXfFXCgsOSHw4aHCd3aNqdnXEsS4loQ1zKKQ8Wl7M07wuJNBygoKaNjbBQ/Pqsr44Z05bROsX78QzAmtJwsodvyuaEqIwPGjIHcXIolnAdveYQ5mTtpGRXBvSmncePwBKIjLz/xfQkXwpgLT3g5p6CE7bmH2X7gMDtyi9ie63xfsfMgBcVlREeG0Sk2mh8N6Mi4wd1I6h1HeFgNY8utKjfGJyyhh6q0NMjNJbvbKdwy8nZWLN3JTcN7ccclp9KmhZvWRy3iY6KIj4ni7IR2x17MyEDTZlIxbRphSUknTg6qKXHbEEVjfMISeqhKTWVHs1iuGXoj3xfCM9cO4bIzOtf/eO6Sc1oa8sEHhIP7xDxxojPePS8Pli499rofFwMzJpTZ8rkhav+AwVybeCNFBYd547yWDUvm4H7GaGqqM9t01y4499yaZ3kWFBw/Pt3WbDHGJyyhh6D8I6Vc/69lHDx0hNmvTuaMtLvd71iX6fbuJiMlJTnJet06pxKvvjzAzJnOe2Ji/LreujFNhbVcQoWrJVI2dRq3rBW25BTy4to3OXPfZugZ5/49dell17TE7p49zvfw8BNbKJXvqdquMcb4jCX0YFeZLPPyIDOTxzqfx9KOQ3lyx4ec/9OLQA/WnEi90cueMQOmTIHp02tuofhxvXVjmhIbhx7sUlKcKnvYMBb2HMpve13OdQdW8eALU5x2hyVSY0KKjUMPZampkJfHtubtuLvPFQzqFMvU0SNgty10ZUxTYxdFg11SEsVt47i11+WEFxfx1LVDiDr/vMYbRWLrmBsTMKxCDwEzfjqRDVtLePHcVnRr26JxP9wmCRkTMCyhB7nM+Z/z4pZiftUrmot+MqLxA7BJQsYEDGu5BLHDJWXc/cluuuft44/z/uqfIGySkDEBw5M7FkWLyDIRWSkia0WkxtkhInKliKiIuL0Ca7zrkfc3sCuqNY8dWELLqVP8HY4xxs88abmUABeraqGIRAKLReR9VV1adScRiQHuADJ9EKep5svNB3h56Q5uGt6LYY/8y9/hGGMCQK0VuuuuR4Wup5GuL3eD1/8MzACKvReecaeguIH0u/EAAA2uSURBVJR7Xv2KU4oPcnebPH+HY4wJEB710EUkXES+AbKBRaqaWW37YKC7qi6o5TgTRCRLRLJycnLqHXRT99B/1/NdURmPvfkQzR96wN/hGGMChEcJXVXLVfUsoBtwjogMrNwmImHATOD/PDjOLFVNVNXE+Pj4+sbcpKW/+xmvfbWLm9scZugZPW10iTHmB3UatqiqeSKSDqQAa1wvxwADgXTXDQ46AfNEZKyq2tx+L8o/UsofP99Hn0O5TFz5Xxv3bYw5jiejXOJFpI3rcXNgFLChcruq5qtqe1VNUNUEYClgydzbMjJI+8NfyWnWkidylxI97X5/R2SMCTCeVOidgdkiEo7zC+ANVV0gIg8AWao6z6cRGgAWzfw3c08Zze37lnHmO//2dzjGmABUa0JX1VXAYDevT6th/5END8tUdfDwUSafPobT8nK4/eZkf4djjAlQNvU/CEybt5a8Uph9709o1qW1v8MxxgQoS+gB7n9vf8b8lYVMOq05AyyZG2NOwtZyCWAHCku4PyOHM77bxK2vPe7vcIwxAc4SeoBSVe59axWFzZrzRP4yIlOn+jskY0yAs5ZLgHo1cycfb8hm2uj+9J0+x9/hGGOCgFXoAWhLTiEPzl/DBYd2cEPYd/4OxxgTJKxCDzBHyyq487VvaF5yhMdfnkrY1rNtRqgxxiOW0APMXz/+ltV78vlnUjwd15xta7UYYzxmLZcAsmzb9zydvoWrejQj5bmHYdw4556ddgNmY4wHrEIPEDkFJdzxnxX0aNeC1AVPOjdezsqC3FxnB2u7GGNqYQk9AJSVV3D7f77mYNFR5t52Hi3PnwIVpU6FPneutV2MMR6xhB4AHl24gaVbv+fJqwY5s0G7JB2ryCdM8G9wxpigYT10P3v9q50898U2fp2zinElu/wdjjEmiDXNhJ6RASkpfr/Y+Nm3OUx5xxlvPvWlqTBxYkDEZYwJTk0zoaelORcd09KOf70RE/2ybd9z2yvL6dsxhqd/eRaRPxrlbHAXlzHGeMCTOxZFi8gyEVkpImtF5IRsIyKTRGSdiKwSkY9FpKdvwvWS1FQYNgzy8o5P3jUl+prU8xfAl5sPcP2/ltGpdTSzbzybmAvPc3rmM2dCcrJdBDXG1I+qnvQLEKCV63EkkAmcW22fi4AWrse3Aq/XdtyhQ4eqX/XvrwqqLVuqLlnivLZkiWpy8rHn7lTdJznZOUZysscf+8mG/dr3vv/ppU9+ptmHiht4EsaYpgbnTnFu86ondyxSoND1NNL1pdX2+bTK06XAdfX/FdNI9uxxvh8+7FTkCxdCUlLt470rq3g4Vkl7UFHrkiW89PS7PNh9BKd1juXl8cNot2q50zcvKICYGKdCT0pqwEkZY5oyj3roIhIuIt8A2cAiVc08ye7jgfdrOM4EEckSkaycnJy6R9sQ1dsjM2ZA69bQv3/dWhypqcfaIpW/AGpJwgfSv2TC3z4irdsILs7byuu3JNGuZTPnl0NmJqxb53y33rkxpgHEKcA93FmkDfAOcLuqrnGz/Trg98AIVS052bESExM1KyurjuE2QEoKfPABmpzMrjE/56uX57Hvp7+gPPFsWkVFOF/REfRo14Le8a1o3iy8YZ+XkcGRBx7i5Wsm8fTK7ykinLuXv834h24j7LzzftjHKnRjTF2IyHJVTXS3rU4Ti1Q1T0TSgRTguIQuIqOA+/AgmTeajAyn6k1NZdUd9/Fy90tY0m0ge3ZVwMgJcBBY9O0JbxOBbm2b06dDDH06tOLUDq3o0zGGU7eto9X0B45V526oKqv35LPo2YW8fspVZK89woVdYrn/85foO/12Z6dzz3W+z5wJS5f66OSNMU1NrRW6iMQDpa5k3hz4EHhUVRdU2Wcw8BaQoqqbPPlgn1bolYk8L48dG3fw2FX3sKBtX2KiIxjeuz3nvfYM5y5bRI9ObQj/ZgWHS8ooLCkj/0gpO3KL2LS/kM05hWzaX8DWnMMcLa/44dBdDmVzSkE2HYYNIa5XV9q0aEZFhXL4aDm7DhaxfPtB9h0qJgw4r2And1w2gHNGX3gsNtf/FACndWNrtBhj6qChFXpnYLaIhOP03N9Q1QUi8gDO1dZ5wGNAK+BNEQHYqapjvRN+PaSlUbroI/5y1d3MujCJiMhw7hhxKhNG9KZVVAScOh7SdjuVdngYbVo0o02LZnRrizP1/oxjhyorr2DXwSNs2l/Apqx1bJ63ia0t27N9Sw4H9pdRXOok+8hwoWub5gzu0YZLTu/Ixad1cPrk1aWmOsMlKx8bY4yX1KmH7k0+qdBdlXn22Cv53Trlq1Zd+NmQbtyb0o8OsdENPu4PCbjycVISxaXlRIQJEeFNc46WMaZxnaxCD60slJbGypVbGb0lhtWtu/DX7Qt5ontRw5K567g/TDiqNrIlOjL8WDJ3N9EoQJYZMMaEvpBabXHJbVO4+Ytc2sZE887Xr3D6e3Mgb1PD+9SejDfPyIAxY05cv7zyl0FWFsyfb6NYjDE+EzIV+kfr9nPDssN06dyOt++8iNPv/b33ptFXrcpnzYL27Z3vVaWlOck8Ls75zMrKfNw457XcXBtnbozxqZCo0N/7Zg+T3ljJgC6xzL7xHNq2bObZrM/6mDLFSc5Tphy/VnnVKj4p6fjRLPPnH9+DN8YYHwj6hP7K0h1MfW8N5yS04/nrE4mJjvTtB06f7iTz6dOd55WTg+D4iUHVE7wNTzTG+FhQj3J5Jn0Ljy7cwMWndeDpa4cQHRl+/IiUxuhX27hyY0wj8tpM0UChqjz2wUaeTt/CmEFdePKqQURWjjSpunhWYyRXG1dujAkQQZfQVZW0WR/z0rYSru4ZxYO/OIvwMDm2Qx1WQPSKpCSbvm+MCQhBl9ABwj7/jN989x33pa9Bbh11/EbrVxtjmqigS+giwtQtiyAzExk2zN/hGGNMwAjKcegycyaSnOyMKjHGGAMEYYUOWFvFGGPcCMoK3RhjzIksoRtjTIiwhG6MMSHCEroxxoSIWhO6iESLyDIRWSkia0XkhCUDRSRKRF4Xkc0ikikiCb4I1hhjTM08qdBLgItVdRBwFpAiIudW22c8cFBVTwVmAo96N0xjjDG1qTWhq6PQ9TTS9VV9Ra8fA7Ndj98CLhHXzUWNMcY0Do966CISLiLfANnAIlXNrLZLV2AXgKqWAflAnJvjTBCRLBHJysnJaVjkxhhjjuPRxCJVLQfOEpE2wDsiMlBV11TZxV01fsK6vKo6C5gFICI5IrLDwzjbAwc83DeU2Hk3LU3xvJviOUPDzrtnTRvqNFNUVfNEJB1IAaom9N1Ad2C3iEQArYHvazlWvKefKyJZNa3/G8rsvJuWpnjeTfGcwXfn7ckol3hXZY6INAdGARuq7TYPuN71+ErgE/XXnTOMMaaJ8qRC7wzMFpFwnF8Ab6jqAhF5AMhS1XnAC8DLIrIZpzL/pc8iNsYY41atCV1VVwGD3bw+rcrjYuDn3g3tOLN8eOxAZufdtDTF826K5ww+Om+/3VPUGGOMd9nUf2OMCRGW0I0xJkQEVEIXkRQR2ehaE+aPbraH5JoxHpz3JBFZJyKrRORjEalxHGowqe28q+x3pYioiAT98DZPzllErnL9vNeKyJzGjtEXPPg73kNEPhWRFa6/55f7I05vEpF/iUi2iKypYbuIyN9cfyarRGRIgz9UVQPiCwgHtgCnAM2AlUD/avvcBvzT9fiXwOv+jruRzvsioIXr8a1N5bxd+8UAnwNLgUR/x90IP+s+wAqgret5B3/H3UjnPQu41fW4P7Dd33F74bwvBIYAa2rYfjnwPs7EzHOBzIZ+ZiBV6OcAm1V1q6oeBV7DWSOmqlBcM6bW81bVT1W1yPV0KdCtkWP0BU9+3gB/BmYAxY0ZnI94cs43A0+p6kEAVc1u5Bh9wZPzViDW9bg1sLcR4/MJVf2ck0+w/DHwb3UsBdqISOeGfGYgJfQf1oNx2e16ze0+epI1Y4KMJ+dd1Xic3+rBrtbzFpHBQHdVXdCYgfmQJz/rvkBfEflSRJaKSEqjRec7npz3n4DrRGQ38D/g9sYJza/q+m+/VoF0k2hP1oPxaM2YIOPxOYnIdUAiMMKnETWOk563iIThLMV8Q2MF1Ag8+VlH4LRdRuL8T+wL19pJeT6OzZc8Oe+rgZdU9QkRScKZqDhQVSt8H57feD2fBVKFXrkeTKVunPjfrh/28XTNmCDgyXkjIqOA+4CxqlrSSLH5Um3nHQMMBNJFZDtOj3FekF8Y9fTv+HuqWqqq24CNOAk+mHly3uOBNwBUNQOIxlnAKpR59G+/LgIpoX8F9BGRXiLSDOei57xq+4TimjG1nrer9fAsTjIPhZ4q1HLeqpqvqu1VNUFVE3CuHYxV1Sz/hOsVnvwdfxfnIjgi0h6nBbO1UaP0Pk/OeydwCYCInI6T0EN9je15wK9do13OBfJV9bsGHdHfV4LdXPX9FueK+H2u1x7A+YcMzg/5TWAzsAw4xd8xN9J5fwTsB75xfc3zd8yNcd7V9k0nyEe5ePizFuBJYB2wGvilv2NupPPuD3yJMwLmG+BSf8fshXP+D/AdUIpTjY8Hfgv8tsrP+inXn8lqb/z9tqn/xhgTIgKp5WKMMaYBLKEbY0yIsIRujDEhwhK6McaECEvoxhgTIiyhG2NMiLCEbowxIeL/AWjVWaahNbfeAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xArr, yArr = loadDataSet('ex0.txt')\n",
    "\n",
    "# 对单点进行估计\n",
    "print(lwlr(xArr[0], xArr, yArr))\n",
    "\n",
    "# 得到所有估计\n",
    "yHat = lwlrTest(xArr, xArr, yArr, 0.03)\n",
    "\n",
    "# 绘图\n",
    "xMat = mat(xArr)\n",
    "srtInd = xMat[:,1].argsort(0)\n",
    "xSort = xMat[srtInd][:, 0, :]\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(xSort[:,1], yHat[srtInd])\n",
    "xMat[:,1].flatten().A[0]\n",
    "ax.scatter(xMat[:,1].flatten().A[0], mat(yArr).T.flatten().A[0], s=2, c='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 岭回归\n",
    "简介：在矩阵 x.Tx 上加上一个 lambda*I 从而是的矩阵非奇异。回归计算变为\n",
    "$$w = (X^{T}X + \\lambda I)^{-1}x^{T}y$$\n",
    "\n",
    "岭回归最先用来处理特征多余样本的情况，现在也用于在估计加入偏差，从而得到更好的估计。\n",
    "\n",
    "这里通过引入 lambda 限制所有 w 之和，能够减少不重要参数，这个在统计学上叫做缩减"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ridgeRegres(xMat, yMat, lam=0.2):\n",
    "    xTx = xMat.T * xMat\n",
    "    denom = xTx + eye(shape(xMat)[1]) * lam \n",
    "    if linalg.det(denom) == 0:\n",
    "        print(\"This matrix is singular, cannot do inverse\")\n",
    "        return \n",
    "    ws = denom.I * (xMat.T * yMat)\n",
    "    return ws \n",
    "\n",
    "def ridgeTest(xArr, yArr):\n",
    "    xMat = mat(xArr); yMat = mat(yArr).T\n",
    "    yMean = mean(yMat, 0)\n",
    "    yMat = yMat - yMean\n",
    "    xMeans = mean(xMat, 0)\n",
    "    xVar = var(xMat, 0)\n",
    "    xMat = (xMat - xMeans) / xVar\n",
    "    numTestPts = 30\n",
    "    wMat = zeros((numTestPts, shape(xMat)[1]))\n",
    "    for i in range(numTestPts):\n",
    "        ws = ridgeRegres(xMat, yMat, exp(i-10))\n",
    "        wMat[i, :] = ws.T \n",
    "    return wMat "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xbed5630>"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "abX, abY = loadDataSet('abalone.txt')\n",
    "ridgeWeights = ridgeTest(abX, abY)\n",
    "# print(ridgeWeights)\n",
    "\n",
    "# 绘图（查看缩减效果）\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(ridgeWeights)\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "岭回归的回归系数变化图\n",
    "\n",
    "lambda 很小时，系数与普通回归一样，lambda 很大时，所有回归系数缩减为0，可以在中间某处找到使结果最好的 lambda"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 前向逐步回归\n",
    "* 可以得到与 Lasso 差不多的效果，单更简单，属于一种贪心算法，即每一步都尽可能减小误差，一开始所有权重都设为1，然后每一步的决策都是对某个权重增加或减少一个很小的值\n",
    "* 主要优点在于可以帮助人们理解现有模型并做出改进。当构建一个模型后，可以运行该算法找出重要特征"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [],
   "source": [
    "def regularize(xMat):\n",
    "    inMat = xMat.copy()\n",
    "    inMeans = mean(inMat, 0)\n",
    "    inVar = var(inMat, 0)\n",
    "    inMat = (inMat - inMeans) / inVar\n",
    "    return inMat\n",
    "\n",
    "def rssError(yArr, yHat):\n",
    "    return ((yArr-yHat)**2).sum()\n",
    "\n",
    "def stageWise(xArr, yArr, eps=0.01, numIt=100):\n",
    "    xMat = mat(xArr); yMat = mat(yArr).T\n",
    "    yMean = mean(yArr)\n",
    "    yMat = yMat - yMean \n",
    "    xMat = regularize(xMat)\n",
    "    m,n = shape(xMat)\n",
    "    returnMat = zeros((numIt, n))\n",
    "    ws = zeros((n,1)); wsTest = ws.copy(); wsMax = ws.copy()\n",
    "    for i in range(numIt):\n",
    "        print(ws.T)\n",
    "        lowestError = inf;\n",
    "        for j in range(n):\n",
    "            for sign in [-1,1]:\n",
    "                wsTest = ws.copy()\n",
    "                wsTest[j] += eps * sign\n",
    "                yTest = xMat*wsTest\n",
    "                rsse = rssError(yMat.A, yTest.A)\n",
    "                if rsse < lowestError:\n",
    "                    lowestError = rsse\n",
    "                    wsMax = wsTest\n",
    "        ws = wsMax.copy()\n",
    "        returnMat[i, :] = ws.T\n",
    "    return returnMat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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    {
     "name": "stdout",
     "output_type": "stream",
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      "[[ 0.044 -0.011  0.12   0.022  2.023 -0.963 -0.105  0.187]]\n",
      "[[ 0.043 -0.011  0.12   0.022  2.023 -0.963 -0.105  0.187]]\n",
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      "[[ 0.043 -0.011  0.12   0.022  2.023 -0.963 -0.105  0.187]]\n",
      "[[ 0.044 -0.011  0.12   0.022  2.023 -0.963 -0.105  0.187]]\n",
      "[[ 0.043 -0.011  0.12   0.022  2.023 -0.963 -0.105  0.187]]\n",
      "[[ 0.044 -0.011  0.12   0.022  2.023 -0.963 -0.105  0.187]]\n",
      "[[ 0.043 -0.011  0.12   0.022  2.023 -0.963 -0.105  0.187]]\n",
      "[[ 0.044 -0.011  0.12   0.022  2.023 -0.963 -0.105  0.187]]\n",
      "[[ 0.043 -0.011  0.12   0.022  2.023 -0.963 -0.105  0.187]]\n",
      "[[ 0.044 -0.011  0.12   0.022  2.023 -0.963 -0.105  0.187]]\n",
      "[[ 0.043 -0.011  0.12   0.022  2.023 -0.963 -0.105  0.187]]\n",
      "[[ 0.044 -0.011  0.12   0.022  2.023 -0.963 -0.105  0.187]]\n",
      "[[ 0.043 -0.011  0.12   0.022  2.023 -0.963 -0.105  0.187]]\n",
      "[[ 0.044 -0.011  0.12   0.022  2.023 -0.963 -0.105  0.187]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[ 0.   ,  0.   ,  0.   , ...,  0.   ,  0.   ,  0.   ],\n",
       "       [ 0.   ,  0.   ,  0.   , ...,  0.   ,  0.   ,  0.   ],\n",
       "       [ 0.   ,  0.   ,  0.   , ...,  0.   ,  0.   ,  0.   ],\n",
       "       ...,\n",
       "       [ 0.043, -0.011,  0.12 , ..., -0.963, -0.105,  0.187],\n",
       "       [ 0.044, -0.011,  0.12 , ..., -0.963, -0.105,  0.187],\n",
       "       [ 0.043, -0.011,  0.12 , ..., -0.963, -0.105,  0.187]])"
      ]
     },
     "execution_count": 205,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xArr, yArr = loadDataSet('abalone.txt')\n",
    "stageWise(xArr, yArr, 0.001, 5000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2., 2.])"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = array([[1,1],[2,2],[3,3]])\n",
    "mean(a,0)"
   ]
  }
 ],
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